In 2 quart saucepan, saute the onions in the olive oil over medium-high heat until the onions are beginning to soften.,Add the mushrooms and saute 5-8 minutes until the mushrooms are soft and the onions are beginning to brown.,Add the sauerkraut and 2/3 Cup of water.,Cover and simmer 15 minutes.,Add the butter and turn off the heat.,(Mixture should be very moist.,Too dry?,Add more water.,I usually have about 1/2 Cup of water resting in the bottom of the pan.,).,______,Stir quickly, then add the milk, 1/2 Cup at a time to reach a consistency a little looser than toothpaste.,(Still holds its shape, but is very soft).,Add the salt, pepper and cheeses and stir well to combine.,In the bottom of a 9x9 pan, add 3-4 lasagna noodles.,Spread 1/3 the potato mixture over the noodles, then 1/3 the sauerkraut.,Repeat layers ending with the last 1/3 of sauerkraut.,This comes right to the top of the pan for me.,Cover tightly with aluminum foil and bake in a 350 degree oven for 45-50 minutes, or until a knife inserted comes out hot.,Let rest 5 minutes.,Cut into 9 squares and serve with dollops of sour cream.